I am a little surprised not to see a decent solution to this problem. So here is mine.
The statement [math]56^{57} > 57^{56}[/math] is equivalent to [math]57 \ln(56) > 56\ln(57)[/math].
Taking quotient we obtain that this is equivalent to [math]\ln(56) / 56 > \ln(57) / 57[/math].
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